It took Draw Something (an iPhone app) 9 days to reach one million users. (source)

In 2000, Napster was the fastest growing application on the Web with 4.9 million at-home Napster users in July, triple the number in January. (source)

In 2005, Skype was the fastest growing application ever going from zero to 54 million customers in 25 months. (source)

In 2007, iLike on the Facebook Platform was the fastest growing application signing up a million users in its first week; then a million more in the 5 days, and another million in the next 4 days. (source)

In 2009, FarmVille on the Facebook Platform was the fastest growing game ever adding more than 1 million active users a week. (source)

In 2011, Instagram's iPhone app reached 12 million users in 12 months. Between January and March of 2012 they added 9 million new users. (source)

In 2012, Angry Birds Space for iOS, Android, Mac and PC was downloaded 10 million times in just three days since its launch. (source)

In 2012, the Draw Something iPhone app reached more than 35 million downloads in just 6 weeks. (source)

It took Angry Birds about 1 year to reach 30 million downloads. Instagram has 27 million users after about 15 months. Draw Something did it in 6 weeks. (source)

Instagram added over a million new users in twelve hours when in launched an Android version of it's mobile application. (source)

Instagram had 5 million downloads on Android in six days. The iOS version of the app took about six months to reach 5 million users. (source)

Why are these growth records being set on new platforms like iOS and Facebook and not the Web? The Web is small pieces loosely joined. Facebook and iOS are the same pieces but they are a lot more tightly joined. In the case of Facebook, things are woven together through the social graph of connections. In the case of iOS, it's the app store, iTunes accounts, and tight OS integrations of these elements that bring things closer together.